* SugarWiki/AwesomeMusic: Neil Innes' songs imitated the Beatles songs so well that they wound up on Beatles bootleg albums, and one fan actually accused him of stealing "Cheese And Onions" from an unreleased Beatle tape. He was ''taken to court'' for the songs, and had to testify that he hadn't listened to the original songs while making the soundtrack, just wrote from memory. There's no way to deny that's stunning.
* HilariousInHindsight: When John Lennon watched the movie, he told them that the songs they did (Get Up and Go in particular) were too close to the real thing and that Paul might sue them. While Paul was fine with the whole project, ATV Music (who owned the rights to the Beatles' music) objected and sued, resulting in half the royalties for all the material going into the Lennon-[=McCartney=] bankbook.
* SuspiciouslySimilarSong: Lots of their work is like this; they cleverly play off of the styles and lyrics of individual songs rather than doing note-for-note parodies. Compare "Back in '64" to "When I'm 64," for instance.
** "Get Up and Go" is probably the closest, following "Get Back's" structure and chord progression so closely that you can sing one over the other.
* TearJerker: Perhaps unexpectedly, "Back in '64".